The period T, of a simple pendulum is dwefined by the function T=4pi rut(l/g) where g is the constant gravitational acceleration and l the length of the pendulum.find the %change in the period caused by lengthening the pendulum by 2%.please help i diffrentiated to get dt/dl=pi/rut lg .I'm stuck there.

mabasamunashe wrote:The period T, of a simple pendulum is dwefined by the function T=4pi rut(l/g) where g is the constant gravitational acceleration and l the length of the pendulum.find the %change in the period caused by lengthening the pendulum by 2%.please help i diffrentiated to get dt/dl=pi/rut lg .I'm stuck there.

Are you using "T" to mean the same thing as "t"? What is the meaning of "rut"? Is this a function name?

The standard equation for a simple pendulum, as displayed in this resource, is given by:

In the above, "L" is defined such that it likely corresponds to your "l", and "g" corresponds to your "g"; the L and g are inside the square root, in ratio. Might this be the equation you are supposed to use? If so, then you may find this discussion, or ones like it, to be helpful.

If I have misinterpreted your meaning, kindly please respond with corrections. Thank you.

mabasamunashe wrote:thus the exact formular now the problem ask to find a %change in the period T given the %change in L length to be 2%.Help me solve the problem.

One of the worked examples at the link was very similar to your exercise. The only difference was that the change was expressed as a fraction rather than as a percentage. Please reply showing how far you got in applying the demonstrated process. Thank you.